Equalizers are known devices used to correct typically the non-linearity of devices such that a transfer function becomes almost linear in a certain range of interest. Such an application is a transmitting device for transmitting audio content to a FM receiver within a short range e.g. several meters in a standard broadcasting range as 88-108 MHz. In such an application it is important that the transmission power is very low as e.g. 11 nW in US.
Throughout the present application we consider that the term “small antenna” refers to an antenna having its physical dimensions much smaller that the wavelength of the signal transmitted via said antenna i.e. the carrier. Let us observe that in known broadcasting systems the antenna dimensions is a fraction of the wavelength of the carrier e.g. ¼, and that in this application we refer to antenna as small as 1/10 or less of the wavelength of the carrier. The problem with small antennas is that they have a very low radiation resistance, which determines in practice a very low efficiency. For example a full size dipole antenna having a length of two times 750 mm and operating at 95 MHz with 50-ohm source impedance has an efficiency of 95% and a source voltage of 200 mV will generate a maximum effective radiated power 100 μW. If we consider a short dipole of two times 50 mm, loaded with coils, we obtain an efficiency of 0.32% depending on the quality factor of the antenna and the position of the coils, the antenna generating an effective radiated power of 250 nW. The radiation resistance for the full size dipole is 70 ohms while the radiation resistance for the short dipole is 0.0052 ohm. Since some kind of electrically loading is required for the short antenna, the antenna becomes narrowband. This is the reason why this kind of antenna radiates a different amount of power at different frequencies.
If this problem is not solved the received signal strength by a FM radio for frequencies besides the resonance frequency is too low for good quality reception and noise will be introduced in the audio signal or it can happen that the received signal will not be detected by the FM radio.